Nicora was born in Varese, Italy and ordained a priest in 1964. Prior to being ordained, he had earned a license in Canon law from the Pontifical Gregorian University in Rome as well as a license in theology from the Theological Faculty in Milan. After his ordination, he became a professor of canon law at the Theological Seminary of Venegano.

Nicora first became a bishop in 1977, when he was appointed auxiliary bishop of Milan and titular bishop of Furnos Minor. Nicora oversaw the 1984 revision of the concordat, between Italy and the Vatican. From 1992 to 1997, he served as bishop of Verona. In 2002, Nicora became President of Administration of the Patrimony of the Apostolic See, where his responsibility was administering the Vatican's income from properties. This position is comparable to that of a chief financial officer in a corporation. Upon the death of a Pope all major Vatican officials automatically lose their positions during a sede vacante, and so Nicora lost his position on 2 April 2005 due to the death of Pope John Paul II but later was confirmed to office by Pope Benedict XVI on 21 April.

On 30 December 2005, the Italian news agency ADN Kronos reported that Nicora was likely to be appointed the Vatican's Cardinal Secretary of State, succeeding Angelo Sodano. However, this did not happen; Tarcisio Bertone became the new Secretary of State.

Pope Benedict XVI appointed Cardinal Nicora Pontifical Legate for the Basilicas of St. Francis and of St. Mary of the Angels in Assisi, without prejudice to his functions as head of the Administration of the Patrimony of the Apostolic See. Having served 10 years as a cardinal-deacon, he was promoted to cardinal-priest by Pope Francis on 12 June 2014.[2]